The present invention relates to methods and systems for determining uncertainty. More specifically, the present invention relates to methods and systems for calculating uncertainty using chordal or dual data.
Measurements and calculations inherently include uncertainty, whether obtained by a human or a machine. Even the most accurate machines, designed to take the most detailed measurements, provide a margin of error when reporting a measurement. Further, calculations performed using similar equations that should theoretically result in the same answer can sometimes provide different answers, thus resulting in a “dependency problem.”
A dependency problem can occur, for example, when performing uncertainty calculations using two or more formula that are similar but produce different results. For example, a formula can be structured as x*(y-z) in a first form and as (x*y)-(x*z) in a second form. While the two formulae should result in the same answer when X, Y, and Z are provided, they may not always provide identical answers, demonstrating that errors can affect all calculations. From a practical standpoint, this implies that one may not in face be free to structure formula or calculations in just any form, even if those formula or calculations should theoretically always arrive at the same answer. Accordingly, there is a continued need for methods to resolve or ameliorate the dependency problem by calculating uncertainty.
In view of the above, Applicant has previously filed a U.S. patent application directed to the use of chordals and duals to provide a new way to effectively and accurately assess error, propagate error and provide uncertainty reporting, see U.S. Publication No. 2016/0132462 (the '462 Application), the entirety of which is incorporated by reference. As discussed in the '462 Application, the duals method has been demonstrated to provide a robust method for performing both small and large-scale computations. It has been shown that the duals method's computational steps are immune to the fatal problems of divide-by-zero and square-root-of-negative seen with traditional computational arithmetic. The duals method also eliminates the dependency problem of uncertainty calculations.
However, current efforts to implement duals arithmetic in commercial computer languages (such as, for example, Excel, MATLAB, Python, mathjs, or LabVIEW) and wide practical applications (such as medical, finance, sports, engineering and science) is hampered by a lack of knowledge of the theory of duals arithmetic and the effective steps needed to create efficient software code. The duals method implementation requires a simpler way to convert all numbers, arithmetic steps and functions to the duals arithmetic format. Thus, there is a need for effective duals method implementation by utilizing built-in mathematical functions common to many software languages.
This present invention satisfies these and other needs through the use of ‘trans-imaginary’ numbers and a computational technique that activates the role of the chordals method in support of duals method implementation.